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Human Conditional Reasoning in Answer Set Programming

Chiaki Sakama

TL;DR

This paper addresses realizing human conditional reasoning within Answer Set Programming (ASP) by introducing modular completion mechanisms for four inference patterns: Affirming Antecedent ($AA$), Affirming Consequent ($AC$), Denying Antecedent ($DA$), and Denying Consequent ($DC$). It defines eight completion types (AC, DC, DA and their default variants) and demonstrates their semantics via answer sets, enabling backward and contrapositive inferences in a principled, context-sensitive way. The authors connect these completions to cognitive psychology tasks (e.g., suppression and Wason selection) and show how they can model abductive explanations, counterfactual reasoning, and neighborhood inference for commonsense AI. The approach preserves ASP's declarative nature while providing a modular, syntax-dependent toolkit to realize pragmatic human-like reasoning and to support broader AI applications in commonsense reasoning. Overall, the work bridges cognitive psychology and ASP by offering a flexible framework to simulate context-driven human reasoning within a well-established logical programming paradigm.

Abstract

Given a conditional sentence "P=>Q" (if P then Q) and respective facts, four different types of inferences are observed in human reasoning. Affirming the antecedent (AA) (or modus ponens) reasons Q from P; affirming the consequent (AC) reasons P from Q; denying the antecedent (DA) reasons -Q from -P; and denying the consequent (DC) (or modus tollens) reasons -P from -Q. Among them, AA and DC are logically valid, while AC and DA are logically invalid and often called logical fallacies. Nevertheless, humans often perform AC or DA as pragmatic inference in daily life. In this paper, we realize AC, DA and DC inferences in answer set programming. Eight different types of completion are introduced and their semantics are given by answer sets. We investigate formal properties and characterize human reasoning tasks in cognitive psychology. Those completions are also applied to commonsense reasoning in AI.

Human Conditional Reasoning in Answer Set Programming

TL;DR

This paper addresses realizing human conditional reasoning within Answer Set Programming (ASP) by introducing modular completion mechanisms for four inference patterns: Affirming Antecedent (), Affirming Consequent (), Denying Antecedent (), and Denying Consequent (). It defines eight completion types (AC, DC, DA and their default variants) and demonstrates their semantics via answer sets, enabling backward and contrapositive inferences in a principled, context-sensitive way. The authors connect these completions to cognitive psychology tasks (e.g., suppression and Wason selection) and show how they can model abductive explanations, counterfactual reasoning, and neighborhood inference for commonsense AI. The approach preserves ASP's declarative nature while providing a modular, syntax-dependent toolkit to realize pragmatic human-like reasoning and to support broader AI applications in commonsense reasoning. Overall, the work bridges cognitive psychology and ASP by offering a flexible framework to simulate context-driven human reasoning within a well-established logical programming paradigm.

Abstract

Given a conditional sentence "P=>Q" (if P then Q) and respective facts, four different types of inferences are observed in human reasoning. Affirming the antecedent (AA) (or modus ponens) reasons Q from P; affirming the consequent (AC) reasons P from Q; denying the antecedent (DA) reasons -Q from -P; and denying the consequent (DC) (or modus tollens) reasons -P from -Q. Among them, AA and DC are logically valid, while AC and DA are logically invalid and often called logical fallacies. Nevertheless, humans often perform AC or DA as pragmatic inference in daily life. In this paper, we realize AC, DA and DC inferences in answer set programming. Eight different types of completion are introduced and their semantics are given by answer sets. We investigate formal properties and characterize human reasoning tasks in cognitive psychology. Those completions are also applied to commonsense reasoning in AI.
Paper Structure (21 sections, 18 theorems, 100 equations, 2 tables)

This paper contains 21 sections, 18 theorems, 100 equations, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Human Conditional Reasoning in ASP
  4. AC Completion
  5. DC Completion
  6. DA Completion
  7. AC and DA as Default Reasoning
  8. Default AC completion
  9. Default DA completion
  10. Characterizing Human Reasoning Tasks
  11. Suppression Task
  12. Wason Selection Task
  13. Applications to Commonsense Reasoning
  14. Abduction and Prediction
  15. Counterfactual Reasoning
  16. ...and 6 more sections

Key Result

Proposition 2.1

Let $\Pi$ be a program and $\Phi=\{\,r\mid r\in\Pi\;\;\hbox{and}\;\; head^+(r)=\varnothing\}$. Also let $\Pi'=(\Pi\setminus \Phi)\cup \{\, \eta(r)\mid r\in\Phi\,\}$. Then $\Pi$ and $\Pi'$ have the same answer sets.

Theorems & Definitions (69)

  • Example 2.1
  • Example 2.2
  • Example 2.3
  • Proposition 2.1: IS98
  • Proposition 2.2
  • proof
  • Example 2.4
  • Proposition 2.3
  • proof
  • Definition 3.1: AC completion
  • ...and 59 more